Wavelengths of Gyrotactic Plumes in Bioconvection

Abstract

Bioconvection occurs as the result of the collective behaviour of many micro-organisms swimming in a fluid and is realized as patterns similar to those of thermal convection which occur when a layer of fluid is heated from below. We consider the phenomenon of pattern formation due to gyrotaxis, an orientation mechanism which results from the balance of gravitational and viscous torques acting on bottom-heavy micro-organisms. The continuum model of Pedley et al.(1988,J. Fluid. Mech . 195, 223–237) is used to describe the suspension. The system is governed by the Navier–Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation. These equations are solved numerically using a conservative finite-difference scheme. To examine the dependence of the horizontal pattern wavelengths on the parameters, we consider two-dimensional solutions in a wide chamber using rigid side walls. The wavelengths of the numerical computations are in good agreement with the experimental observations and we provide the first computational examples of the commonly seen ‘bottom-standing’ plumes.